S. R. Faruqi:

It's obvious that the wound in the heart that would be devoid of burning, is a wound with a 'black spot' [suvaidā]. Thus another meaning comes to be, 'that black-spotted wound through which the light of the Divine radiance would not be reflected on the heart, is not a cause for pride, but rather a cause for regret and sorrow'.

With regard to the wound's being without burning, for the 'inner-self to burn' is very fine. Ghalib has used metaphors of this kind in two verses. It's possible that these might be the gift of Mir, but it's also entirely possible that they might have spontaneously occurred to Ghalib, because Ghalib too, like Mir, was a king of wordplay:

G{143,2},

and

G{230,3}.

The latter verse is worthy to be counted among the best not only of Ghalib's verses, but of verses in the Urdu language. But Mir too composed such a powerful second line that even in the presence of Ghalib's verse its lamp shines.

For the wound in the heart to be without burning is just as if the house would be without a lamp. In this there are several meanings:

(1) A person's true/original home is his heart.

(2) The wound of the heart is to the heart, as to a father is 'the pupil of his eye' [=his child]. (A child is called 'the lamp of the house'.)

(3) We can also read Mir's first line like this: be-soz-e dāġh , dil par gar jī jale bajā hai . Now the meaning becomes, 'at a heart that is devoid of the burning of a wound, if the inner-self would burn, then it's proper'.

(4) Among bajā , dil , jī there's the connection of a zila, because for the heart or inner-self to remain 'in its place' is called bajā rahnā . To put so much into a simple-seeming verse is a high order of eloquence [balāġhat].

Jalal [Lakhnavi] has tried to light his own flame from the lamp of Mir and Ghalib. His verse is somewhat strained; it seems that he had a little difficulty in managing the refrain. Even so, the verse is a good one:

vuh dil naṣīb huʾā jis ko dāġh bhī nah milā
milā vuh ġham-kadah jis ko chirāġh bhī nah milā

[that heart was vouchsafed, which did not receive even a wound
that grief-chamber was received, which did not receive even a lamp]

In contrast to this, Mir himself, in his own informal style, has well said, in the second divan [{916,6}]:

adh jalā lālah sāñ rahā to kyā
dāġh bhī ho to koʾī bā al-kul ho

[if it remained half-burned, like a tulip, then so what?
if there would be even/also a wound, then let it be some complete one]

FWP:

SETS == IZAFAT
MOTIFS == HOME
NAMES
TERMS == WORDPLAY

In the first line, thanks to the clever deployment of the (metrically optional) izafat, be-soz plays a versatile role . It can be read either as an adjective describing the wound in the heart (1a), or else as followed by an izafat, as part of an adverbial phrase, 'without the burning of a heart-wound' (1b).